Long-term Dynamics of the Electron-nuclear Spin System of a Semiconductor Quantum Dot

Abstract

A quasi-classical theoretical description of polarization and relaxation of nuclear spins in a quantum dot with one resident electron is developed for arbitrary mechanisms of electron spin polarization. The dependence of the electron-nuclear spin dynamics on the correlation time ${\tau }_c$ of electron spin precession, with frequency $\Omega$, in the nuclear hyperfine field is analyzed. It is demonstrated that the highest nuclear polarization is achieved for a correlation time close to the period of electron spin precession in the nuclear field. For these and larger correlation times, the indirect hyperfine field, which acts on nuclear spins, also reaches a maximum. This maximum is of the order of the dipole-dipole magnetic field that nuclei create on each other. This value is non-zero even if the average electron polarization vanishes. It is shown that the transition from short correlation time to $\Omega {\tau }_c>1$ does not affect the general structure of the equation for nuclear spin temperature and nuclear polarization in the Knight field, but changes the values of parameters, which now become functions of $\Omega {\tau }_c$. For correlation times larger than the precession time of nuclei in the electron hyperfine field, it is found that three thermodynamic potentials ($\chi$, $\mathbf{\xi }$, $\varsigma$) characterize the polarized electron-nuclear spin system. The values of these potentials are calculated assuming a sharp transition from short to long correlation times, and the relaxation mechanisms of these potentials are discussed. The relaxation of the nuclear spin potential is simulated numerically showing that high nuclear polarization decreases relaxation rate.

RevTeX 4, 12 pages, 9 figures

References in corpus (5)

• Hyperfine interaction in a quantum dot: Non-Markovian electron spin dynamics
• Theory of electron spin decoherence by interacting nuclear spins in a quantum dot
• Semiclassical dynamics and long time asymptotics of the central-spin problem in a quantum dot
• Hyperfine interaction induced decoherence of electron spins in quantum dots
• Exactly solvable spin dynamics of an electron coupled to large number of nuclei and the electron-nuclear spin echo in a quantum dot

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• Spin dynamics of a confined electron interacting with magnetic or nuclear spins: A semiclassical approach
• Hanle effect in (In,Ga)As quantum dots: Role of nuclear spin fluctuations
• Unveiling the electron-nuclear spin dynamics in an n-doped InGaAs epilayer by spin noise spectroscopy
• Temperature dependence of electron-spin relaxation in a single InAs quantum dot at zero applied magnetic field
• Spin-orbit coupled particle in a spin bath
• Loschmidt echo driven by hyperfine and electric-quadrupole interactions in nanoscale nuclear spin baths
• Dynamical nuclear spin polarization in a quantum dot with an electron spin driven by electric dipole spin resonance